Cremona's table of elliptic curves

2142 = 2 · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	2142d	Isogeny class
Conductor	2142	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-3197988864 = -1 · 212 · 38 · 7 · 17	Discriminant
Eigenvalues	2+ 3-  2 7+  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,9,-2723]	[a1,a2,a3,a4,a6]
j	103823/4386816	j-invariant
L	1.3060323407156	L(r)(E,1)/r!
Ω	0.65301617035779	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17136bl1 68544bf1 714f1 53550dx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	2	+	0	-6	+	0	8	6	-8	10	6	12	0	10	8	6	12	0	-6	-8	-16	-2	2

---

Quadratic twists for elliptic curve 2142d1

-4	8	-3	5	-7	17
17136bl1	68544bf1	714f1	53550dx1	14994bg1	36414bh1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations